Question

 The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are λ= 10 calls per hour. Determine the following probabilities:

Answer 1

for Poisson distribution:

$P(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}$

for example, probability to get 2 calls per hour:

$P(x=2)=\frac{10^2e^{-10}}{2!}=0.0023$